Problem: What do the following two equations represent? $2x+3y = -3$ $2x+3y = 3$
Putting the first equation in $y = mx + b$ form gives: $2x+3y = -3$ $3y = -2x-3$ $y = -\dfrac{2}{3}x - 1$ Putting the second equation in $y = mx + b$ form gives: $2x+3y = 3$ $3y = -2x+3$ $y = -\dfrac{2}{3}x + 1$ The slopes are equal, and the y-intercepts are different, so the lines are parallel.